What is the fundamental frequency of a guitar string that is 1 m long, the mass per unit length is 50 g/m and the Tension in the string is 50 N.
2 Answers
An alternate method is to recognize that for a string fixed at both ends the wavelength is 2 times the length of the string. In that case you have a wavelength of 2 m.
The relationship between the string tension F(T), the m/L ratio and the velocity of the wave is: F(T) = m/L * v^2
Solving for the velocity gives 31.62 m/s.
Since v = frequency * wavelength; 31.62 m/s divided by 2 m = 15.81 Hz as the fundamental frequency.
As you can see, in physics there is often more than one way to end up with the correct answer.
We have to find the fundamental frequency of a string. The formula for the fundamental frequency of a stretched string is given by
sqrt [ T/ (m/L)]/ 2*L , where T is the tension in the string, m is the mass per length and L is the length of the string.
Using the values given to us:
L = 1m
m= 50g /m = .05 Kg/m
T = 50 N
Therefore sqrt [ T/ (m/L)]/ 2*L
=> sqrt [ 50/ (.05/1)]/ 2*1
=> sqrt [ 50 / .05] / 2
=> sqrt 1000 /2
=> 31.62 / 2
=> 15.81 Hz
Therefore the fundamental frequency is 15.81 Hz